The article “Low-Temperature Heat Capacity and Thermodynamic Properties of 1,1,1-trifluoro-2, 2-dichloroethane” (R. Varushchenko and A. Druzhinina, Fluid Phase Equilibria, 2002:109–119) presents measurements of the molar heat capacity (y) of 1,1,1-trifluoro-2,2-dichloroethane (in J · K−1 · mol−1) at several temperatures (x) in units of 10 K. The results for every tenth measurement are presented in the following table.
y
|
x
|
y
|
x
|
5.7037
|
1.044
|
60.732
|
6.765
|
16.707
|
1.687
|
65.042
|
7.798
|
29.717
|
2.531
|
71.283
|
9.241
|
41.005
|
3.604
|
75.822
|
10.214
|
48.822
|
4.669
|
80.029
|
11.266
|
55.334
|
5.722
|
|
|
a. Fit the simple linear model y = β0+ β1x + ε. Make a residual plot, and comment on the appropriateness of the model.
b. Fit the simple linear model y = β0 + β1 ln x + ε. Make a residual plot, and comment on the appropriateness of the model.
c. Compute the coefficients and their standard deviations for polynomials of degrees 2, 3, 4, and 5. Make residual plots for each.
d. The article cited at the beginning of this exercise recommends the quartic model y = β0 +β1x +β2x2 +β3x3 + β4x4 + ε. Does this seem reasonable? Why or why not?